At a council meeting on Tuesday night, a motion was put forward by Greens councillor Sophie Wade to explore "ways to make travelling on Yarra's streets more equitable."
According to the ABC, Cr Wade put forward the motion due to concerns for public safety.
"We know that those vehicles have a much higher likelihood of killing and injuring people than regular vehicles do," Cr Wade said.
"For children, they're eight times more likely to kill a child when they hit them than a regular vehicle."
The councillor also said that the area's infrastructure wasn't built to support these vehicles.
"We've got smaller streets, they were designed to the 1800s," she said, adding "They weren't designed for this kind of vehicle, and it's something that we need to look at everywhere."
The motion was unanimously carried, with members of the public also speaking in favour of the motion.
Councillor Stephen Jolly described any Hummer owner living in Yarra City suburbs such as Collingwood or Fitzroy as "an absolute idiot" that needs to be dealt with.
Councillor Jolly also passed amendments asking for more data, saying "We need to know how many SUVs, RAMs, Defenders, Hummers are on the streets of Yarra, how many accidents are coming from these vehicles, how many fines are we charging as a result of a large oversized vehicle taking two parking spots."